In the prior art of geometric models, and in the particular area of polyhedral frameworks, structures are known which comprise a single completed coherent membranal surfaces, or singular planar framework. These structures can be said to be one sided in that they have an exterior polyhedral surface which provides the form by which the object is defined. Examples would be called twelve-sided or twenty-sided or the like. The interior of all prior polyhedrons can only be said to be the underside of the exterior form, having identical planes and edges, and therefore have the same structure inside and outside. These structures of the prior art define a singular exterior form, and the interior void space remaining has an essentially identical perimeter to that of the initial polyhedron minus the dimension of the depth of the structure, either membrane or framework. In addition, models of the prior art are conceived of as essentially comprised of combinations of linear vectors, or strut members, which combine to create the geometry of the given model. Polyhedral models have been developed which are unique in their geometry, are self-referential in that they are entirely mathematical in conception and advantage, and therefore, exist in a kind of pure conceptual mathematical domain, which is far removed from the pragmatic reality of the world of engineering and architectural structures. Essentially then, the prior art of polyhedral models is in many ways an elegant discipline which unfortunately does not have a meeting point or correspondent level with that of the practical world. Complex Polyhedral models are beautiful but curiously unusable constructs.
An example of this separation of concept and pragmatics may be shown by examining the work of R. Buckminister Fuller, in particular his Geodesic Domes. These models, advanced the teaching in the field of Solid Geometry by providing structures which had greater strength per unit weight than structures previously known. But, because they are conceived of as essentially shell-like structures, their use in reality shows serious limitations. The outside of the structure is always an elegant triangulated framework shell structure, but upon entering the inside space created by this structure, one will find a traditional rectilinear post and beam-like structure built within the Geodesic Dome. This interior structure is completely separate from the shell both conceptually and structurally. This is because the Geodesic Domes solve one problem only, that of skin or exterior. But they do not consider the problem of the housing of and differentiation of interior volumes to satisfy other requirements of storage, either of material storage, or human occupation, nor the implications of these further needed requirements in regards to gravity. Of course this also means that in the prior art the exterior loads such as roof loads, winds loads, and earthquake loads, are carried in the exterior shell structure according to the prior art, and the interior structural loads, floor loads, etc. are carried by the separate interior structure. This, of course is a non-unified way of comprising a functional structure, and it is obvious that under severe loading conditions, the two different structural systems may indeed deflect or act in conflict with each other. What is needed is a model having some of the advantages of the triangulated framework shell structures similar to that known in the prior art, but also having some additional interior differentiation and interior structure, that is united to the exterior frame.
These problems are also present in the other prior art models of solid geometry particularly that of polyhedral models, and they have therefore not found a domain of convenient or efficient usage in engineering or architectural practice.
No polyhedrons have been developed with the specific purpose of housing functions of different type, whether that be two chemicals of different nature or spaces divided into circulation and various other occupancies for human architectural or other usage.
The prior art has evolved from empirical work done centuries ago, to the present, but only using several known methods. These methods include stellation, and the formation of dual models. These methods always rely on the formation and building of a polyhedron from the inside and proceeding outward. Building upon the known, the prior art has found only advances that are extensions of the known art. This simple but critical impediment has limited the advance of the catalog of known polyhedrons. It is because of this bias that no substantially different polyhedrons have been developed. What is need is a different method of generating new polyhedrons.
No single device or model of the prior art can by using only one step, form both a rigid exterior framework and a differentiated interior structure which forms several different interior spaces, all of which is rigid and united to the exterior framework. Such a unified structure is needed.